Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def binary(l, n):
    low, high = 0, len(l)
    while low <= high:
        mid = (low+high)//2
        if(l[mid] == n):
            return True
        elif(l[mid] > n):
            high = mid-1
        else:
            low = mid+1
    return False

l = list()
for i in range(1, 50000):
    l.append((i*(i+1))//2)
n = int(input())
i = 0
result = False
while l[i] <= n:
    if(binary(l, n-l[i])):
        result = True
        break
    i += 1
if result:
    print("YES")
else:
    print("NO")